Learning time of linear associative memory

Neural networks can be used as associative memories which can learn problems of acquiring input–output relations presented by examples. The learning time problem addresses how long it takes for a neural network to learn a given problem by a learning algorithm. As a solvable model to this problem we analyze the learning dynamics of the linear associative memory with the least-mean-square algorithm. Our result shows that the learning time τ of the linear associative memory diverges in τ ∝ (1 – ρ)^–2 as the memory rate ρ approaches 1. It also shows that the learning time exhibits the exponential dependence on ρ when ρ is small.